Poisson sampling for spectral estimation in periodically correlated processes

Vincent Monsan

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Displaying similar documents to “Poisson sampling for spectral estimation in periodically correlated processes”

An asymptotic approximation of Wallis’ sequence

Vito Lampret (2012)

Open Mathematics

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An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, $W (n) \cdot (a_{n} + b_{n}) < π < W (n) \cdot (a_{n} + b_{n}^{'})$ with $a_{n} = 2 + \frac{1}{2 n + 1} + \frac{2}{3 {(2 n + 1)}^{2}} - \frac{1}{3 n {(2 n + 1)}^{'}} b_{n} = \frac{2}{33 {(n + 1)}^{2^{'}}} b_{n}^{'} \frac{1}{13 n^{2^{'}}} n \in ℕ$ .

Canonical coordinates for coadjoint orbits of completely solvable groups.

Arnal, Didier, Ben Ammar, Mabrouk, Currey, Bradley N., Dali, Béchir (2005)

Journal of Lie Theory

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Rademacher variables in connection with complex scalars.

Seigner, J.A. (1997)

Acta Mathematica Universitatis Comenianae. New Series

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On the Kuramoto-Sivashinsky equation in a disk

Vladimir Varlamov (2000)

Annales Polonici Mathematici

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We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed...